Is there any damage from deep discharge, ignoring the low batt. indicator, and using it until it dies?
Is there any damage from toping off the tank even though it doesn't need charging and is only slightly depleted?

I hope that you know that the 700 have replaceable rechargeable battery. You can go and buy a pair of Sanyo Eneloop (slow discharge). All those batteries can handle a limited number of charge discharge and the newer on can go up to 2100 times.

Yes I am aware you can replace the battery but I'd like to maximize its use before I have to do that. Different chemistries such as sealed Lead acid, Ni-MH, LSD-NiMH, Ni-Cad, Li-Po, etc have different charging characteristics and different ways to treat them to optimize their re-charge cycles.

The batts that came with mine I believe are Ni-MH, but they don't specify being LSD Ni-MH, like Eneloops, however I hope they are. GP Recyko makes a charger and their instructions say"

Remove the batteries and unplug the charger once the

charging is complete. Do not leave batteries in the charger for extended periods.

Which makes me think over charging IS a risk {not of danger but of longest possible battery life and number of charge cycles}

In A/V reproduction accuracy, there is no concept of "accounting for taste". We don't "pick" the level of bass, etc., any more than we pick the ending of a play. High fidelity means an unmodified, neutral, exact copy (or "reproduction") of the original artist's tonal balance, timing, dynamics, etc..

The way I counted is the following:
- each battery can be recharged 2100 times (the 1st gen could be recharged 1000 times)
- if you had to recharge the battery every 2 weeks it would make 26 recharge per year
- battery would last you 80 years

Even at the cost of $5 per battery (the current cost is $14 a pack of 4), I will not worry about the cost of it.

As for safety, the remote will shutdown when it detect low battery so will not let you discharge it completely.
And for charging the internal charge circuit seem to shutdown the charge when it think the battery is full (the battery is cold, meaning that it stop charging), so I think that it is pretty safe. In any case I think that NiMH battery can handle over charge better than Li-ion batteries.

I upgraded my DirecTV equipment this weekend and for some reason my 700s are lagging when controlling the mini Genies (C41W-100). I have to press a button 4-5 times before anything happens on the screen. The 700 that controls the HR44 Genie works fine. The DirecTV remotes work fine when controlling the minis. Has anyone else had this issue?

Also, lets say I was playing PS4 the last time I used my system. The next time I turn everything and want to watch TV, the input does not change. I have to press help in order for it to change to the right input. I know I have to adjust the delay, but I have no idea which one.